1. Field of the Invention
The invention relates multidimensional measurement data evaluations with respect to geometrical tolerances, particularly by using best-fitting type algorithms and accounting for uncertainties of measurement.
2. Description of Related Art
Measurement data concerning the geometric dimensions of test parts can be acquired by using many different types of measuring instruments, including both contacting and non-contacting forms of measurement. Multiple data points associated with individual test parts are generally related to each other through a common datum of the measuring instrument.
Metrology programs for accepting or rejecting manufactured test parts compare the measured data points of the test parts to an ideal or nominal definition (also referred to as a nominal model boundary) of the test parts straddled by geometric tolerance zones that specify how much the measured data points can deviate from the ideal part definition and still be accepted. Best-fitting algorithms collectively fit the measured data points of the test parts to the ideal definition of the test parts. In making the best collective fit for the measured data points, the common frame of reference of the measured data points is adjusted with respect to the frame of reference of the ideal part definition.
Many best-fitting algorithms find the orientation of the measured data points with respect to the ideal part definition at which the measured data points collectively deviate from the ideal part definition by a least amount. This can be a good solution if the tolerances for all the part dimensions are equally balanced about the ideal part definition. However, such best-fitting algorithms that converge toward the ideal part definition can reject test parts, as having one or more measured data points out of tolerance, that might otherwise be fit within the tolerances.
A non-linear optimization approach proposed in U.S. Pat. No. 6,665,080 to Haertig et al. is carried out on a point-by-point basis to best fit all of the data points within the geometric tolerances. In other words, all of the data points are fit within the tolerance boundaries (i.e., within a tolerance zone) as best as possible without particular regard for the ideal definition of the part.
The reliability of the measured data points to represent actual dimensions of a test part also affects the reliability of the determinations as to whether measured test parts are actually within the tolerance zone. Measurement errors can lead to erroneous conclusions that some measured test parts are within the tolerance zone when they are not and other measured parts are not within the tolerance zone when they are. To reduce such errors, measurement uncertainties have been quantified, which allows for statistically better test part evaluations to be made.
The uncertainties of the test part measurements depend on a number of factors such as the accuracy of the measuring instruments, environmental conditions during the measurements, the properties of artifacts, the knowledge of metrologists, and measurement techniques. The uncertainties can vary for each point of measurement. Standards have been developed to estimate the uncertainties and to apply the uncertainties to the acceptance or rejection of test parts against known tolerances.
Applying the estimated uncertainties to the fitted data allows more statistically accurate measurement results. Based on Gaussian error estimates, each measured point can be associated with an uncertainty range corresponding to a particular confidence interval. For example, the uncertainty range of a measured point can be set to correspond to a confidence interval of 95 percent covering a range of values within two standard deviations of the measured value. A so-called acceptance zone can be defined by contracting the tolerance zone boundaries on either side of the ideal part definition through a guard band corresponding to one-half of the uncertainty range. Measured points found within the acceptance zone have at least a 95 percent chance of actually being within the tolerance zone. Test parts in which all measured points fit within the acceptance zone are generally accepted as being within tolerance.
Uncertainty zones straddle the tolerance boundaries by one-half of the uncertainty range on each side. Measured points within the uncertainty zone cannot be determined to be either inside or outside the tolerance zone with the desired level of confidence. Test parts having measured points within the uncertainty zone are generally not accepted as being within tolerance. Test parts having measured points beyond the uncertainty zone are rejected as being out of tolerance.
Often the results of best fitting techniques and subsequent uncertainty analyses of measured data points are used to make decisions about the acceptance, non-acceptance, or rejection of test parts as well as on corrective actions needed to accept the parts. The rejection or non-acceptance of test parts that might actually be within tolerance or the acceptance of parts that might actually not be within tolerance can have significant consequences.